# How do you find the critical point(s) of #f(x,y) = (x-y)^2#?

##### 1 Answer

The critical points of a two-variables functions are to be found using the gradient.

The gradient is a vector which has dimension equal to the number of variables: in this case, 2.

The coordinates of the gradient are the derivatives with respect to each variable the function depends on. In this case, the vector will be a 2-dimensional vector, where the first coordinate is the derivative with respect to

Note that deriving with respect to a variable means to consider the other as a constant.

Now, expand the square in the definition of

Deriving with respect to

Deriving with respect to

Now, critical points of a functions are the points in which the gradient equals the zero vector. This happens if the following system is solved:

Both equations yield the line